Geometry & Topology Volume 29, issue 4 (2025)

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ISSN (print): 1465-3060

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The systole of large genus minimal surfaces in positive Ricci curvature

Henrik Matthiesen and Anna Siffert

Geometry & Topology 29 (2025) 1819–1849

DOI: 10.2140/gt.2025.29.1819

Bibliography

1	N S Aiex, Non-compactness of the space of minimal hypersurfaces, Math. Ann. 370 (2018) 191 MR3747485
2	F Balacheff, H Parlier, S Sabourau, Short loop decompositions of surfaces and the geometry of Jacobians, Geom. Funct. Anal. 22 (2012) 37 MR2899682
3	O Chodosh, C Mantoulidis, Minimal surfaces and the Allen–Cahn equation on 3-manifolds : index, multiplicity, and curvature estimates, Ann. of Math. 191 (2020) 213 MR4045964
4	O Chodosh, D Ketover, D Maximo, Minimal hypersurfaces with bounded index, Invent. Math. 209 (2017) 617 MR3681392
5	H I Choi, R Schoen, The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature, Invent. Math. 81 (1985) 387 MR807063
6	H I Choi, A N Wang, A first eigenvalue estimate for minimal hypersurfaces, J. Differential Geom. 18 (1983) 559 MR723817
7	T H Colding, W P Minicozzi II, Embedded minimal disks: proper versus nonproper, global versus local, Trans. Amer. Math. Soc. 356 (2004) 283 MR2020033
8	T H Colding, W P Minicozzi II, The space of embedded minimal surfaces of fixed genus in a 3-manifold, I : Estimates off the axis for disks, Ann. of Math. 160 (2004) 27 MR2119717
9	T H Colding, W P Minicozzi II, The space of embedded minimal surfaces of fixed genus in a 3-manifold, II : Multi-valued graphs in disks, Ann. of Math. 160 (2004) 69 MR2119718
10	T H Colding, W P Minicozzi II, The space of embedded minimal surfaces of fixed genus in a 3-manifold, III : Planar domains, Ann. of Math. 160 (2004) 523 MR2123932
11	T H Colding, W P Minicozzi II, The space of embedded minimal surfaces of fixed genus in a 3-manifold, IV : Locally simply connected, Ann. of Math. 160 (2004) 573 MR2123933
12	T H Colding, W P Minicozzi II, The Calabi–Yau conjectures for embedded surfaces, Ann. of Math. 167 (2008) 211 MR2373154
13	T H Colding, W P Minicozzi II, The space of embedded minimal surfaces of fixed genus in a 3-manifold, V : Fixed genus, Ann. of Math. 181 (2015) 1 MR3272923
14	D Fischer-Colbrie, R Schoen, The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature, Comm. Pure Appl. Math. 33 (1980) 199 MR562550
15	M Freedman, J Hass, P Scott, Least area incompressible surfaces in 3-manifolds, Invent. Math. 71 (1983) 609 MR695910
16	M Gromov, Systoles and intersystolic inequalities, from: "Actes de la Table Ronde de Géométrie Différentielle" (editor A L Besse), Sémin. Congr. 1, Soc. Math. France (1996) 291 MR1427763
17	R Hardt, L Simon, Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. of Math. 110 (1979) 439 MR554379
18	K Irie, F C Marques, A Neves, Density of minimal hypersurfaces for generic metrics, Ann. of Math. 187 (2018) 963 MR3779962
19	H B Lawson Jr., Complete minimal surfaces in S³, Ann. of Math. 92 (1970) 335 MR270280
20	Y Liokumovich, F C Marques, A Neves, Weyl law for the volume spectrum, Ann. of Math. 187 (2018) 933 MR3779961
21	F C Marques, A Neves, Existence of infinitely many minimal hypersurfaces in positive Ricci curvature, Invent. Math. 209 (2017) 577 MR3674223
22	F C Marques, A Neves, Morse index of multiplicity one min-max minimal hypersurfaces, Adv. Math. 378 (2021) 107527 MR4191255
23	F C Marques, A Neves, A Song, Equidistribution of minimal hypersurfaces for generic metrics, Invent. Math. 216 (2019) 421 MR3953507
24	W H Meeks III, J Pérez, A Ros, Limit leaves of an H lamination are stable, J. Differential Geom. 84 (2010) 179 MR2629513
25	D A Neumann, 3-manifolds fibering over S¹, Proc. Amer. Math. Soc. 58 (1976) 353 MR413105
26	R Schoen, Estimates for stable minimal surfaces in three-dimensional manifolds, from: "Seminar on minimal submanifolds" (editor E Bombieri), Ann. of Math. Stud. 103, Princeton Univ. Press (1983) 111 MR795231
27	R Schoen, S T Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. 110 (1979) 127 MR541332
28	R Schoen, S T Yau, The existence of a black hole due to condensation of matter, Comm. Math. Phys. 90 (1983) 575 MR719436
29	A Song, Existence of infinitely many minimal hypersurfaces in closed manifolds, Ann. of Math. 197 (2023) 859 MR4564260
30	J L Tollefson, 3-manifolds fibering over S¹ with nonunique connected fiber, Proc. Amer. Math. Soc. 21 (1969) 79 MR236945
31	B White, Curvatures of embedded minimal disks blow up on subsets of C¹ curves, J. Differential Geom. 100 (2015) 389 MR3343836
32	X Zhou, On the multiplicity one conjecture in min-max theory, Ann. of Math. 192 (2020) 767 MR4172621